On subrings of amalgamated free products of rings

James Renshaw

Colloquium Mathematicae (1999)

  • Volume: 79, Issue: 2, page 241-248
  • ISSN: 0010-1354

Abstract

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The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.

How to cite

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Renshaw, James. "On subrings of amalgamated free products of rings." Colloquium Mathematicae 79.2 (1999): 241-248. <http://eudml.org/doc/210639>.

@article{Renshaw1999,
abstract = {The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.},
author = {Renshaw, James},
journal = {Colloquium Mathematicae},
keywords = {amalgams; coproducts; strong embeddability; purity; faithful flatness},
language = {eng},
number = {2},
pages = {241-248},
title = {On subrings of amalgamated free products of rings},
url = {http://eudml.org/doc/210639},
volume = {79},
year = {1999},
}

TY - JOUR
AU - Renshaw, James
TI - On subrings of amalgamated free products of rings
JO - Colloquium Mathematicae
PY - 1999
VL - 79
IS - 2
SP - 241
EP - 248
AB - The aim of this paper is to develop the homological machinery needed to study amalgams of subrings. We follow Cohn [1] and describe an amalgam of subrings in terms of reduced iterated tensor products of the rings forming the amalgam and prove a result on embeddability of amalgamated free products. Finally we characterise the commutative perfect amalgamation bases.
LA - eng
KW - amalgams; coproducts; strong embeddability; purity; faithful flatness
UR - http://eudml.org/doc/210639
ER -

References

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  1. [1] P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959), 380-398. Zbl0087.26303
  2. [2] J. M. Howie, Embedding theorems with amalgamation for semigroups, Proc. London Math. Soc. (3) 12 (1962), 511-534. Zbl0111.03702
  3. [3] J. M. Howie, Subsemigroups of amalgamated free products of semigroups, ibid. 13 (1963), 672-686. Zbl0124.01701
  4. [4] J. H. Renshaw, Extension and amalgamation in rings, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), 103-115. Zbl0589.16019
  5. [5] J. H. Renshaw, Extension and amalgamation in monoids and semigroups, Proc. London Math. Soc. (3) 52 (1986), 119-141. Zbl0546.20054
  6. [6] J. H. Renshaw, Perfect amalgamation bases, J. Algebra 141 (1991), 78-92. Zbl0735.20041
  7. [7] J. H. Renshaw, Subsemigroups of free products of semigroups, Proc. Edinburgh Math. Soc. (2) 34 (1991), 337-357. Zbl0752.20036
  8. [8] J. R. Rotman, An Introduction to Homological Algebra, Pure and Appl. Math. 85, Academic Press, New York, 1979. Zbl0441.18018

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